Most of the ones I applied to said on the status page (or elsewhere) that applications weren't considered until they were complete (which includes receiving all LORs). However, since you received one (and I know UMich & Pitt send out auto-invites pre-secondary/pre-LORs), it does happen. It probably just depends on the school.
Ok, yea Pitt didn't need mine either so I think it was pretty much an auto although I don't think they have defined cutoffs like umich since it took them a few days whereas mich was instant before i even had to fill out a secondary, in fact I submitted two and a half weeks ago to pitt and I'm still not complete, it's taking them forever to add the letters.